Looking at this first-order differential equation, I am embarrassed to admit
how much time I've spent trying to figure out an approach that can yield a
closed form solution. It is a much simplified version of a more complicated
model, which we usually solve by numeric integration, and I had hoped to
illustrate how the simple version could still yield qualitative insights.
However, perhaps I'm missing something obvious, but I can't seem to get it
into a solvable form.
For what it's worth, the time constant k in the exponential is << 1 in
non-dimensional units. All the coefficients are constants.
p[t]*y[t] + y'[t] == q[t]
p[t_] = (A1 + A2/E^(k*t))/(A3 - a1/E^(k*t) - a2*t)
q[t_] = -((Cb*(A4 + A5/E^(k*t)))/(A3 - a1/E^(k*t) - a2*t))
With apologies if it's trivial and thanks for any suggestions.
A. Sharma
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Atul Sharma MD, FRCP(C)
Pediatric Nephrologist,
McGill University/Montreal Children's Hospital